Andersen casement windows show condensation and ice on the inside of the glass

I replaced the widows in my house this spring, and you're asking a lot of the same questions I asked.

First, the cost of the windows themselves is only part of the equation. You also need to consider the removal of the old windows, installation of the new ones, and the finish work - because chances are, all the trim, and all of the interior sills will also need to be replaced. Installation can actually be 50% of the cost of the job, and a poor installation will ruin any value you might get from buying a top-notch window.

There are a few things to consider when looking at the windows themselves. First, as you point out, is the construction. I ended up going with vinyl - again, a quality vinyl window and a cheap vinyl window are two different things - the local shop here had examples of a number of different windows cut open so you can see the difference. Cheap windows may not be insulated, or may be made up of different pieces glued together, rather than a single extruded piece.

Next, the glass. You can get single, double, or even triple panes. Some use argon between the panes, some don't - the sealed, argon-filled windows offer better insulation. Then there's the low-e coating on the glass - it can be applied in different ways, which will affect the durability and effectiveness of the window.

You need to consider casement vs single hung vs double hung. Are they on a 2nd or 3rd story? You'll probably want to get a window that allows you to clean the outside without having to get up on a ladder - most double-hung windows will allow you to clean it from the inside of the house. If you're putting windows into a bedroom, you have to allow for a certain size for egress - you may need to go with a casement window in that case.

The bottom line is, check around - get at least 3 estimates, unless you're planning on installing them yourself. See what's included in the estimate - one of our estimates included a single line item for "Installation", while another had 3 pages of details, down to the number of board-feet of trim, cans of foam insulation, and the cost of the building permit. Guess which one we went with?

I think this probably has more to do with regional building habits than any systematic optimal decision. I agree, what you call "tilt and turn" windows seem to be more common in Europe. In the US (and elsewhere?) a similar style is a "casement" window, although it's not as functional (doesn't open as far and doesn't offer multiple ways of opening).

I have seen "tilt and turn" windows used in the US in basements, since they can satisfy emergency egress requirements. Perhaps they are less common in general use because they are more complicated / expensive? The latching and hinging mechanisms are much more complicated than a sash window, which typically is just held in place by friction.